一个关于高斯整数的最小正整数问题  

Problem of the smallest positive integer related to Gaussian integer

作　　者：朱小林[1] 贺君燕[2] 

机构地区：[1]上海海事大学基础部,上海200135 [2]上海电力学院数理系,上海200090

出　　处：《纯粹数学与应用数学》2008年第1期45-48,共4页Pure and Applied Mathematics

基　　金：国家自然科学基金(10471104);上海市科教委基金(03JC14027)

摘　　要：主要讨论了高斯整数多项式所表整数的计算,利用初等数论基本理论和方法,获得了一个含有n(n≥1)个高斯整数常量和变量的线性多项式虚部所表整数中最小正整数的精确显式表达,并进一步获得了该多项式虚部所表整数的全体.This paper mainly discusses the computation of integers represented by Gaussian integer polynomial. Using the basic theories and methods in elementary number theory, the smallest positive integer, represented by the imaginary part of a linear polynomial which has n（n ≥ 1） Gussian integer constants and Gussian integer variables, is accurately characterized. Furthermore, the all integers represented by the imaginary part of this polynomial are obtained.

关 键 词：高斯整数 最小正整数 最大公约数 

分 类 号：O156.1[理学—数学] O156.2[理学—基础数学]